Gauging system for sculptured surfaces

ABSTRACT

An arrangement for removing excess material from an object surface, to provide a desired finished surface. Holes are drilled into the object so that the bottoms of the holes lie on the desired finished surface. The holes have a shape so that the observed hole diameter at the prevailing surface of the object is dependent on the hole depth and thereby dependent on the amount of material remaining to be removed between the prevailing surface and the desired finished surface. The prevailing surface is continuously observed and measured, and the depths of material to be removed in a sequence of steps is calculated dependent on the measurements of the prevailing surface and the coordinates of the desired finished surface. As a result of the calculations, the depth of material removed during each step is controlled, so that upon carrying out a sequence of such steps, the surface exposed on the object after the last step has been carried out, coincides with the desired finished surface. The accuracy of the material removal equipment may be substantially less than the accuracy of the finished surface. Grooves instead of circular holes are cut when the radius of curvature of both the prevailing and desired surfaces becomes sufficiently small, so as to provide sufficient definition of the desired surface. With the grooves, the observed parameter is groove width rather than hole diameter.

BACKGROUND OF THE INVENTION

This is a continuation-in-part of the parent application Ser. No.157,435 filed June 9, 1980, now U.S. Pat. No. 4,337,566.

An automated system for finishing (grinding, sanding, milling, etc.) offlat, contoured or complex sculptured surfaces requires a high degree ofpositional dexterity in the finishing equipment. Such dexterity (asfound typically in industrial robots) is usually accompanied by limitedabsolute positional accuracy in the equipment. If finishing accuraciesfor the final surface are to be greater than the absolute positionalaccuracy of the finishing equipment, then some type of active feedbackcontrol mechanism must be implemented. This mechanism must monitor thematerial thickness left to be removed and thereby modify and stop thematerial removal process at the proper level.

SUMMARY OF THE INVENTION

The present invention provides this feedback function via continuousoptical sensing of holes previously drilled into the surface. The bottomof the holes lies on the desired finished surface. The shape of theholes is such that the observed hole diameter at the material surface isproportional to the hole depth, and therefore, also proportional to theamount of material remaining to be removed. A simple optical sensor andassociated signal processing can continuously observe the surface andprovide the "depth to go" feedback based upon the observed holediameter.

The depth to which the holes are drilled below the initial surface iscontrolled by data obtained from an external measurement system. Thissystem must have measurement accuracy equivalent to the desired finishedsurface accuracy. An accurate coordinate map of the initial surface isthus provided by this measurement system. The distance (normal to thesurface) between this map and the desired finished surface provides thedepth required for each hole. The holes can be drilled to an accuratedepth by the less accurate finishing equipment, by employing an accuratedepth control stop (referenced to the surface) on the drill mechanismitself.

Thus, the entire finishing process can be implemented using materialremoval equipment of relatively poor accuracy but high dexterity. Theultimate system accuracy is provided by the external measurement system.The latter equipment exhibits high accuracy at the expense of dexterity,and is not a part of the present invention.

The novel features which are considered as characteristic for theinvention are set forth in particular in the appended claims. Theinvention itself, however, both as to its construction and its method ofoperation, together with additional objects and advantages thereof, willbe best understood from the following description of specificembodiments when read in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of the essential elements of the arrangementin accordance with the present invention;

FIG. 2 is a block diagram and shows the basic operation carried out bythe central computer in FIG. 1;

FIG. 3 is a schematic view and illustrates the parameters from which theamount of material to be removed is calculated;

FIG. 4 is a diagrammatic view of a milling cutter or drill used toremove material;

FIG. 4a is a graphical representation of the relationship between holediameter and depth characteristic, when using the milling cutter of FIG.4;

FIG. 5 is a schematic view of a drilling mechanism and optical sensorwhereby the accuracy of the drilling depth is achieved by appropriatereferencing to the object surface.

FIG. 6 is a geometrical diagram and shows the interrelationships ofparameters used in conjunction with the arrangement of FIG. 5;

FIG. 7 is a perspective view of an object having a small radius ofcurvature along an edge into which grooves are cut;

FIG. 8 is a plan view of the arrangement for cutting the grooves in FIG.7;

FIG. 9 is a side view of the arrangement of FIG. 8;

FIG. 10 is a diagrammatic view and shows the geometrical relationshipsfor achieving precise groove depth, in accordance with the presentinvention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

An overall block diagram of the system is shown in FIG. 1. It operatesin conjunction with an external measurement subsystem 10 capable ofmeasuring the 3-D surface coordinates to the accuracy required of thedesired finished surface. This subsystem 10 can also measure theposition of reference marks 12 on the surface.

The external measurement subsystem 10 measures the objects' unfinishedsurface, creating a 3-D surface map. The data 14 describing this surfacemap is fed into the finishing system central computer 16.

Based on a reference pattern algorithm operating on the inputted surfacemap, the computer directs a robot manipulator 18 (via controller 20) toplace a reference grid pattern on the object surface using its markerstylus. The external measurement system 10 measures the precise portionof these grid marks on the surface. The data describing these referencemark positions is fed into the finishing system central computer 16.

The desired 3-D finished surface map is transferred to the computer froma storage medium 22. The computer calculates the "excess material"between the unfinished and desired finished surfaces at each referencemark position, and commands the robot 24 to drill holes into the objectsurface to a depth equal to the excess material calculated at thatpoint. The entire object surface is then painted.

The computer commands the robot, thereupon, to grind the surface toremove excess material. The initial grinding pattern is determined by aspecial control algorithm operating on the computed excess material map.This first pass with the grinder removes all surface point except thatleft in the holes. This provides the contrast required to make the holesvisible to the grinder vision system 26. Thereafter, the vision systemon the grinder observes the depth of the remaining holes (i.e., theexcess surface material) and thus updates the excess material map. This,in turn, causes the grinding pattern to be continuously modified tosmoothly and evenly bring the object surface down to the desiredfinished surface. When the holes are no longer visible, the grindingprocess is terminated.

The external measurement subsystem 10 has an accuracy capabilityequivalent to the desired surface finish accuracy. It provides, as inputto the finishing system, a map 14 of the measured surface of the objectto be finished as well as the coordinates 12 of reference markspreviously placed on the object surface. This data is provided in any3-D coordinate system convenient to the measurement subsystem, and istransposed by the central computer 16 to the coordinate system of thefinishing equipment 24, 28, 44 (the robot). This transposition requiresthat the position and orientation in space of the measurement subsystemto be known with respect to the finishing system. Normal surveyingtechniques will provide this relationship to the accuracy required. Theexternal measurement subsystem can be implemented in any of a number ofways, and is not part of the present invention. It can even be meanswhereby the measurements are carried out manually.

The desired finish surface map is fed to the central computer 16 fromany convenient mass storage medium 22, such as magnetic tape. Itdescribes the desired 3-D coordinates of the finished surface of theobject in any convenient coordinate system. In practice, the lattercoordinate system would usually be related in some manner to the objectitself. For instance, an object having an axis of revolution might mostconveniently be described in a cylindrical coordinate system centered onthat axis. In the central computer 16, the desired surface map data istransposed into the coordinate system of the finishing equipment 24, 28,44.

In FIG. 2, the basic operations of the central computer 16 are shown inblock diagram form. The measured surface map (from the externalmeasurement subsystem 10) and the finished surface map (from the massstorage medium 22) are transposed to the finishing system coordinates asdescribed above. These transposed maps are denoted as s_(o) and s_(f)respectively. The computer also calculates the surface normals (θ_(N))to s_(f) at each point on the desired finished surface. The measuredsurface (s_(o)) and the normals to the finished surface (θ_(N)) areinputs to both the reference mark/drill pattern subroutine and the grindpattern subroutine. In the former subroutine s_(o), in conjunction witha stored pattern generation algorithm, determines the reference markeror drill position for the robot. Angles θ_(N) determine the orientationin space of the marker or drill. In the latter subroutine, so, inconjunction with a grinding pattern algorithm, determines the positionand maneuvering of the grinder 30 in space. The angles θ_(N) determineits orientation in space, and assures that grinding is always donenormal to the desired surface.

As material is removed, the grinding pattern is modified by an excessmaterial map. This describes the excess material vs. position on thesurface. It controls the grinding pattern to remove this material in amanner so as to slowly and evenly bring the object surface down to thedesired surface. The initial excess material map ΔS_(o) /S_(R) isgenerated from s_(o), s_(f) and θ_(N) as shown in FIG. 3. Excessmaterial is defined as the distance between surface s_(o) and s_(f)along the line 32 which is normal to the desired surface s_(f). Theexcess material is calculated at each reference mark point S_(R) whosecoordinates are supplied by the external measurement subsystem. Thecalculated excess material at these points ΔS_(o) /S_(R) provides boththe depth data for drilling of the reference holes, as well as theinitial excess material map.

The vision system 26 in the grinder 30 continuously observes thediameter of the holes as grinding takes place. These diameters arerelated to the excess material remaining in the manner described in FIG.4. The hole diameter (i.e. excess material) information is fed to thecomputer by loop 34 to continually update the excess material map andthus modify the grinding pattern accordingly. As indicated in FIG. 4, amilling cutter 36 designed with a ball end tip and a tapered body willresult in a hole diameter vs. depth characteristic which is advantageousfor this application. The effective control loop feedback gain isproportional to change in hole diameter resulting from a change indepth, i.e., ∂D/∂ΔS. FIG. 4 shows this function to be a constant fordepths greater than a critical depth Δs_(c) and inversely proportionalto Δs for depths less than Δs_(c). Thus, feedback gain is increased asthe excess material becomes small. This provides tighter control overthe final phases of the grinding process, thus preventing the removal oftoo much material. The selection of the cutter parameters R and θ (FIG.4) can optimize the feedback gain characteristics for the particularapplication.

Referring to FIG. 4, the relationship between hole diameter and depthmay be obtained as follows: ##EQU1##

The graphical relationship between the parameters is shown in FIG. 4a.

The ultimate accuracy of the finished surface depends on the accuracywith which the reference holes can be drilled so that the sphericalbottom of the hole lies tangent to the desired finished surface. This,in turn, depends on two factors. First, the calculation of ΔS_(o) /S_(R)defined by FIG. 3 must be accurate. Since it can be assumed that boththe desired surface and the mathematical computation of ΔS_(o) /S_(R)can be as accurate as required, the accuracy of the measured surfaceS_(o) is the only concern. Thus, the system is limited by the accuracyof the external measurement subsystem. The second factor in achievingproper hole depth is dependent on the implementation of the drilligprocess. Ideally, the drill axis must be colinear with the normal lineof FIG. 3, and the drill bottom must penetrate to exactly the desiredsurface and no further. The robot manipulator 18, however, does not havethe absolute positional accuracy to achieve either of theserequirements. These limitations are largely overcome by theimplementation shown in FIGS. 5 and 6.

In FIG. 5, a schematic view of the drilling mechanism and optical sensoris shown. The milling bit 38 is rotated by a drill motor 60 and ismovable along its axis of rotation by a vertical drive motor 62 and gearmechanism 64. The drill reference post 40 serves to provide a referencepoint A which is placed on the object surface by the robot manipulator.A vertical compliant bushing 66 provides mechanical relief in thevertical direction. In conjunction with the pressure sensor 42 feedbackto the computer 16, this mechanism 44 assures that the reference point Ais placed on the object surface by the robot 24 with the proper force.

The imaginary plane through point A and normal to the drill axis is theO depth reference plane. This plane is identical to the x, y plane shownin FIG. 6. Level gauges 46 and 48 (FIG. 5) contain spring loadedplungers which place reference points B & C on the object surface.Electrical mechanisms (such as potentiometers) which sense the extensionof the plungers, provide for locating reference points B and C withrespect to the x, y plane of FIG. 6. If the object surface is assumedreasonably flat between points A, B and C, then the locations of pointsB and C fully define the object surface in the drill x, y, z coordinatesystem.

An optical sensor 50 is mechanically affixed to the drill so that itsoptical axis and field of view provide visibility of the object surfacebetween points A, B and C. This sensor (typically a TV camera) willsense and locate the reference mark S_(R) which was previously placed onthe surface and for which the excess material data is given inaccordance with FIG. 3. A ray through the known optical sensor node andpoint S_(R) is thus defined. The intersection of this ray with theobject surface defined by points A, B and C thus locates reference pointS_(R) in x, y, z space. Most particularly, the displacement ΔS_(R) ofS_(R) in the z direction, i.e. above or below the x, y (O depthreference) plane, is defined.

The drill axis is oriented by the robot manipulator to be perpendicularto the desired surface shown as the x', y' plane of FIG. 6. It may beassumed that the desired surface is reasonably flat over this smallregion of interest. Then, the distance along the drill center linebetween the desired surface (x', y' plane) and the O depth reference (x,y) plane is defined to be ΔS_(o) /S_(R) +ΔS_(R). The milling bit istherefore to be driven vertically to a depth of ΔS_(o) /S_(R) +ΔS_(R)below the O depth reference plane. This will bring the ball end of themiller precisely tangent to the desired surface at point E of FIG. 6.The inaccuracy of the drill placement in x, y and the slope of theobject surface with respect to the desired surface have thus beenproperly compensated for by the arrangement in accordance with thepresent invention.

The drill depth control feedback is achieved by units 50 and 52 inFIG. 1. Parameters α, β defined by the geometry in FIG. 6, are fed tocomputer 16 by the vision unit 50, as shown in FIG. 1. Similarly,parameters b and c in FIG. 6 are supplied to the computer by unit 52.The blocks in FIG. 1 are conventional elements known in the art, and thefunctions performed by these blocks can even be carried out manually byhand, and manual sensing and observation, for example.

An essential feature of the present invention, therefore, is that thematerial removal equipment need not have an absolute positional accuracywhich is equal to the accuracy of the desired finished surface. Sensingof the diameters of the holes is carried out in real time to providefeedback control for the grinding or material removal process.

The automated finishing process according to the present invention isapplicable not only to grinding, but to other finishing methodsincluding sanding, milling and other abrasive material removalmechanisms.

The hole diameters, as observed by the vision system 26, can bedetermined either by a two-dimensional pattern analysis or bythree-dimensional measurement. The former method requires only a singlecamera, but it is necessary to paint the surface prior to the beginningof material removal. This latter process can be eliminated by using athree-dimensional sensor in the form of a camera and projector, withappropriate processing.

When the radius of curvature of both the prevailing and desired surfacesbecomes sufficiently small, the spacing between holes must be decreased,so that the desired surface becomes defined with sufficient accuracy.Under these conditions, the holes eventually tend to encroach upon oneanother, and the process becomes considerably inefficient. When thisoccurs, an alternate arrangement can be implemented to define accuratelythe desired surface, by placing continual grooves in the surface. Thesegrooves are oriented so as to intersect the desired surface in the planeof greatest curvature, as shown in FIG. 7, where the relationship amongthe grooves suddenly cut into article 72 to obtain the desired surface74 upon observing the prevailing surface 76.

If the grooves are cut with a helical cutter as indicated, the bottom ofthe groove 70 will be round-shaped, as in the case of using holes. Thischaracteristic, therefore, retains the relationship between excessmaterial to be removed and the observed diameter, which is used in thearrangement with holes. In the case of grooves, the observed parameteris groove width rather than hole diameter. The groove is effectively ancontinuum of holes along the direction of high curvature.

The accurate cutting of a groove 70 so that its bottom 80 follows thedesired surface 74 can be achieved by the arrangement shown in FIGS. 8and 9. These Figs. show, respectively, a top or plan view and side viewof a helical cutter 78 cutting grooves 70 in the edge of a typicalobject or article 72. The tool edge (depth) stop 82 is placed on theobject surface, and the y axis drive 84 moves the cutter 78 into thesurface to a predetermined depth with respect to the prevailing edge 76.By continually tilting the entire mechanism and modifying the y axisdrive (tool spindle), as shown in FIG. 9, a smooth and continuous grooveis cut in the object edge 86.

Control of the y axis drive so that the precise groove depth ismaintained is achieved by the arrangement shown in FIG. 10. At any pointon the desired surface 74, a normal 88 to the desired surface tangent 90can be established and a line 92 perpendicular to this normal andtangent to the prevailing surface thus defined. The distance (Δ) betweenthe two surface tangents 90, 92 is the depth to which the cutter 78 mustpenetrate beyond the edge depth stop 82 when the axis mechanism isparallel to the normal. Thus a cutting depth is associated with eachangle of attack of the grooving mechanism. The depth Δ is calculated bythe computer 16 based upon the stored data describing the prevailing anddesired surfaces. At the same time, the translation of the cuttingmechanism in a direction along the cutter axis will not affect groovedepth. Thus absolute cutter position in this direction need not beaccurately maintained.

Without further analysis, the foregoing will so fully reveal the gist ofthe present invention that others can, by applying current knowledge,readily adapt it for various applications without omitting featuresthat, from the standpoint of prior art, fairly constitute essentialcharacteristics of the generic or specific aspects of this invention,and therefore, such adaptations should and are intended to becomprehended within the meaning and range of equivalence of thefollowing claims.

What is claimed is:
 1. A method for removing material from an object toprovide a desired finished surface having at least a portion with asubstantially small radius of curvature, comprising the steps of:cutting grooves into the object so that the bottoms of the grooves lieon the desired finished surface, said grooves having a shape so that theobserved groove width at the prevailing surface of the object isdependent on the groove depth and thereby dependent on the amount ofmaterial remaining to be removed between the prevailing surface and thedesired finished surface; observing and measuring the prevailingsurface; calculating depths of material to be removed in a sequence ofmaterial removing steps dependent on measurements of the prevailingsurface and desired finished surface; controlling the depth of materialremoved from said calculated step during each of said material removingsteps; and carrying out said material removing steps in sequence so thatafter the completion of the last step the surface exposed on the objectcoincides with the desired finished surface; said grooves being cut atleast in said portion having a radius of curvature sufficiently smallbelow a predetermined magnitude for defining said desired finishedsurface with a predetermined accuracy.
 2. A method as defined in claim1, wherein the accuracy of said material removing steps is substantiallyless than the accuracy of the desired finished surface.
 3. A method asdefined in claim 1, wherein parameters of said grooves are measured inreal time prior to or during each material removal step.
 4. A method asdefined in claim 1, wherein said material removal steps comprise totalmilling steps.
 5. A method as defined in claim 1, wherein said materialremoval steps comprise standing steps for removing material byabrasives.
 6. A method as defined in claim 1, wherein widths of saidgrooves are observed by a two-dimensional pattern measurement.
 7. Amethod as defined in claim 1, wherein widths of said grooves areobserved by a three-dimensional measurement.
 8. An arrangement forremoving material from an object to provide a desired finished surface,comprising: means for cutting grooves into the object so that bottoms ofthe grooves lie on the desired finished surface, said grooves havingshape so that the observed groove width at the prevailing surface of theobject is dependent on the groove depth and thereby dependent on theamount of material remaining to be removed between the prevailingsurface and the desired finished surface; means for observing andmeasuring the prevailing surface; means for calculating depths ofmaterial to be removed in a sequence of material removing stepsdependent on measurements of the prevailing surface and desired finishedsurface; means for controlling the depth of material removed from saidcalculating step during each of said material removing steps; and meansfor carrying out said material removing steps in sequence so that afterthe completion of the last step the surface exposed on the objectcoincides with the desired finished surface; said grooves being cut atleast in said portion having a radius of curvature sufficiently smallbelow a predetermined magnitude for defining said desired finishedsurface with a predetermined accuracy.
 9. An arrangement as defined inclaim 8, wherein said means for carrying out said material removingsteps has an accuracy substantially less than the accuracy of thedesired finished surface.
 10. An arrangement as defined in claim 8,wherein widths of said grooves are measured in real time prior tocarrying out said material removing steps.